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Answered

Forming a committee of 5 from 15 members of a club​

Sagot :

Answer:

C(15,5) = 3003

Step-by-step explanation:

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[tex]\large{\tt{1:42\:pm\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:3/1/22}}[/tex]

[tex]\huge{\blue{\boxed{\gray{\mathbb{ANSWER}}}}}[/tex]

Forming a committee of 5 from 15 members of a club

[tex]\\[/tex]

[tex]\huge{\red{\boxed{\gray{\mathbb{SOLUTION}}}}}[/tex]

  • [tex]_15C_5 = \dfrac{15!}{(15 - 5)! 5}[/tex]

  • [tex]= \dfrac{15!}{10! 5!}[/tex]

  • [tex]= \dfrac{15 × 14 × 13 × 12 × 11 × \cancel{10} × \cancel{9} × \cancel{8} × \cancel{7} × \cancel{6} × \cancel{5} × \cancel{4} × \cancel{3} × \cancel{2} × \cancel{1}}{\cancel{10} × \cancel{9} × \cancel{8} × \cancel{7} × \cancel{6} × \cancel{5} × \cancel{4} × \cancel{3} × \cancel{2} × \cancel{1} × 5 × 4 × 3 × 2 × 1}[/tex]

  • [tex] = 3003[/tex]

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